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doctoral thesis
Obratne Edmundson-Lah-Ribaričeve nejednakosti i srodni rezultati
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:154315
Mikić, Rozarija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Mikić, R. (2017). Obratne Edmundson-Lah-Ribaričeve nejednakosti i srodni rezultati (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:154315

Mikić, Rozarija. "Obratne Edmundson-Lah-Ribaričeve nejednakosti i srodni rezultati." Doctoral thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:154315

Mikić, Rozarija. "Obratne Edmundson-Lah-Ribaričeve nejednakosti i srodni rezultati." Doctoral thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:154315

Mikić, R. (2017). 'Obratne Edmundson-Lah-Ribaričeve nejednakosti i srodni rezultati', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 27 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:154315

Mikić R. Obratne Edmundson-Lah-Ribaričeve nejednakosti i srodni rezultati [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2025 March 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:154315

R. Mikić, "Obratne Edmundson-Lah-Ribaričeve nejednakosti i srodni rezultati", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:154315

Metadata
TitleObratne Edmundson-Lah-Ribaričeve nejednakosti i srodni rezultati
Title (english)Converse Edmundson-Lah-Ribarič inequalities and related results
AuthorRozarija Mikić
MentorJosip Pečarić (mentor)
Committee memberSanja Varošanec (predsjednik povjerenstva)
Committee memberMario Krnić (član povjerenstva)
Committee memberMirna Rodić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-05-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
Definirat će se nova klasa funkcija koja proširuje klasu 3-konveksnih funkcija za koju će se dokazati generalizacija Levinsonovog tipa Edmundson-Lah-Ribaričeve nejednakosti. Dokazat će se da analogne generalizacije vrijede i za Edmundson-Lah-Ribaričevu nejednakost za hermitske operatore u Hilbertovom prostoru, te za skalarni produkt istih. Dalje, promatrat će se Jensenova i Edmundson-Lah-Ribaričeva nejednakost za linearne funkcionale. Dobit će se njihovi obrati u obliku razlike, kao i... More profinjenja i poboljšanja spomenutih obrata. Dobiveni rezultati primijenit će se na generalizirane sredine i na neke poznate nejednakosti (Hölderovu, Hermite-Hadamardovu, Giaccardijevu i Petrovićevu nejednakost). Dobit će se i obrati Jensenove i Edmundson-Lah-Ribaričeve operatorske nejednakosti, kao i daljnja profinjenja i poboljšanja istih. Dobiveni opći rezultati primijenit će se na kvazi-aritmetičke operatorske sredine, te na potencijalne operatorske sredine. Također će se dobiti i obrati Andove i Davis-Choijeve nejednakosti za pozitivna linearna preslikavanja, te Edmundson-Lah-Ribaričeva nejednakost i njen obrat u obliku razlike za pozitivna linearna preslikavanja. Dokazat će se i obrati u obliku razlike i kvocijenta za poseban tip poopćenih koneksija - solidarities koji uključuje i koneksije, te za relativnu operatorsku entropiju. Less
Abstract (english)
A new class of functions that extends the class of 3-convex functions will be defined, and Levinson’s type generalization of the Edmundson-Lah-Ribarič inequality will be proved for those functions. Analogue generalizations of the Edmundson-Lah-Ribarič inequality for self-adjoint operators in Hilbert space and for their scalar product will be proved. Next, inequalities of Jensen and Edmundson-Lah-Ribarič for positive linear functionals will be studied. New inequalities of difference... More type, as well as their refinements and improvements, will be obtained. These results will be applied to generalized means and some famous inequalities (the ones of Hölder, Hermite-Hadamard, Giaccardi and Petrović). Further, converses of the Jensen and Edmundson-Lah-Ribarič operator inequalities and their refinements and improvements will be obtained. General results will be applied to quasi-arithmetic operator means and to potential operator means. Finally, converses of Ando’s and Davis-Choi’s inequality, as well as the Edmundson-Lah-Ribarič and its converse of difference type for positive unital mappings, will be studied. Ratio and difference type converses will be proved for a special type of solidarities which includes connections, and for relative operator entropy. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:154315
Study programmeTitle: Mathematics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resourceText
Extent106 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-03-19 10:19:03
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